Kiwi kapers 3

Relationship between the width of the IQR for sample medians of sample size n and the population IR and the sample size…  IQR for sample medians (sample size = n) is approximately of the population IQR

Developing an informal confidence interval for the population median…  For our informal confidence interval for the population median we want to use  Sample median  Sample IQR/  n  We need to see how big to make this interval so we’re pretty sure the interval includes the population median  We want it to work about 90% of the time

 Remember we’re in TEACHING WORLD  We’re going to explore how wide our intervals should be when we can work backwards from a given population.

 Informal confidence intervals… sample median  k x sample IQR/  n  What would be the ideal number ( k ) of sample IQR/  n to use all the time to be pretty sure the interval includes the population median? 3 different samples n = 30 3 different medians 3 different IQRs

That is…  We know what the population median actually is  We can look and see how far away from the population median this is: sample IQR/sqrt(n)

Worksheet 2 Deciding how many sample IQR/n we need for the informal confidence interval (finding k ) For each example… 1. Mark the sample median on the big graph and draw a line to the population median 2. Find the distance the sample median is from the population median (2.529kg) 3. Divide by sample IQR/  n  This gives the number of sample IQR /  n that the sample median is away from the population median  THIS IS THE NUMBER WE ARE INTERESTED IN

1. Mark the sample median on the big graph and draw a line to the population median 2. Find the distance the sample median is from the population median (2.529kg) 3. Divide by sample IQR/  n

EG 4) EG 5) EG 6) EG 7) EG 8) EG 9) EG 10) / = / = / = Divide by sample IQR/  n This gives the number of sample IQR/  n that the sample median is away from the population median

From our 10 samples it would appear ±1.5 x IQR/sqrt(n) would be most effective. That is… it should capture the population median most of the time / = / = / = Divide by sample IQR/  n This gives the number of sample IQR/  n that the sample median is away from the population median

Collect the Summary Statistics for 5 samples of 30 kiwis. Plot the ‘box’ plot (no whisker) for each sample On your plot draw three lines (in three different colours), showing… median  1 x IQR/  n median  1.5 x IQR/  n median  2 x IQR/  n Does using the median  1.5 x IQR/  n look about right? More Samples Fathom link to generate 5 samples

How many out of the 5 samples have the population median within the interval if : a) ± 1 x the interval b) ± 2 x the interval c) ± 1.5 x the interval Getting the population Median in the interval

The final formula for the informal confidence interval is : Final formula for informal Confidence interval